{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "629863db-489f-4c84-89f8-e2f2a97086c6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True parameters: slope = 3, intercept = 2\n",
      "Iteration 0: Loss = 112.0616\n",
      "Iteration 100: Loss = 1.0078\n",
      "Iteration 200: Loss = 0.8183\n",
      "Iteration 300: Loss = 0.8150\n",
      "Iteration 400: Loss = 0.8149\n",
      "Iteration 500: Loss = 0.8149\n",
      "Iteration 600: Loss = 0.8149\n",
      "Iteration 700: Loss = 0.8149\n",
      "Iteration 800: Loss = 0.8149\n",
      "Iteration 900: Loss = 0.8149\n",
      "Estimated parameters: slope = 3.0138, intercept = 1.8962\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0: Loss = 129.6323\n",
      "Iteration 0: Loss = 62.9508\n",
      "Iteration 0: Loss = 69.3483\n",
      "Iteration 0: Loss = 84.5824\n"
     ]
    },
    {
     "data": {
      "image/png": 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9e1qzTrURGhp62rFW9xp33HGHXn31Ve3du1c//PCDnnnmmdO61vTp01VSUlKpMMzIyNC0adP0+OOP64YbbpDD4fA4tqqcOPfccyWVNw9xfdYtW7ZUenq69u3b51VcvXr1UlZWln788Udr3/vvv6+wsLBKM7Gn83m7Gi+sWLHC2rdp0yaFhISoR48euuiii2Sz2Srl7sGDB/X5559Xyt2aYrj00ksVEhKizMxMrVq1SjfccIN1rC4+q3//+9/68ccflZubqy+++EJ79+61CpjaXKO699GjRw999NFHKi0ttfbNmTNHd9xxh6Tyv1+lpaUKDQ21rhESEqL09HR+BwCC2Bk1s+Tpv+YdPXpUV155pX7729/qX//6l2677Tbdc889evbZZ60xNS3b+/vf/66xY8daU/dffPGFevbsqfT0dIWEhGjcuHG6//779fTTT9f5ewIagy+//FKZmZmV9iUnJ7v9F2BfjB07Vo8++qhGjRql+++/XydOnNDdd9+t8847T+Hh4ercubN++ctfatq0adZ/5Pj973+vs88+W4MGDar0Wn369NFLL72k8847T7m5uYqIiNBVV11VYwxNmjTRjBkz9Pvf/17NmzfXBRdcoPT0dJ04cULTpk077fd4qv/7v/+rtIxIKv8szznnHM2ZM0dDhgzRAw88oKFDh+rDDz/UQw89pH/961+SpISEBH3//fd69dVX1bRpUz311FPavHmz1zMh/tKkSRM988wzmjx5ss466yzl5eUpJSXF56KhRYsWuv322/XEE0/o7rvvVtOmTZWQkKD33ntPgwcP1q5duzR37lxJqtRFUSrPifvuu0+rV6+WzWbT119/rVtvvVUdO3bUr3/9a02ePFn5+flq06aNHnvsMf33v//1+v8LJk+erIyMDF1zzTWaNWuWdu/erQcffFC//e1vlZiYWCdd1oYMGaIhQ4ZoypQpKikpUZMmTXTffffphhtusGZVx40bp3vvvVdlZWVKSkrSnDlz1KZNG/3mN7/x+johISH65S9/qYceekiSdPHFF1vH6uKzatKkiT7//HO98sor6tKli4qKitS2bVvFxcXV2TWmT5+uiy++WDfeeKNuu+02ZWdn65VXXrGK7IEDB6p///4aO3asHn74YUVHR+v+++9XSUlJncxQAwgQ/98mFXiSrAYPL774omnVqpUpKyszxhizevVqk5iYWOl81020npSUlJhWrVpZN5V6sn79epOQkFA3wQONSFXd8HSyC9mpfG3wYEz5zd0jRowwTZo0MQkJCebWW281R48etY4XFhaau+++2yQkJJjY2FhzzTXXeLwJ/9tvvzXDhg0zUVFRpnnz5ubZZ5+t1ftNT083ycnJJiIiwgwcONDs2LGjVu+jOtV9lpMnT7bO++c//2nOPfdcExERYX72s59Valhx7NgxM3r0aNOsWTPTtm1bc9ttt5mJEyea1NRU66Z2103sVfH0PVXVBEHVNHjw9N5c/24/+eSTpmnTpiY2NtbYbDYjySQkJHjd1OCn3fCMKf9uo6KizB//+EdjjDEffvih6dGjh4mOjjYXXHCBWbJkiUlISHB7b6WlpWbKlCkmLi7OREREVGpkcfz4cXPnnXeaxMRE07RpU3PFFVdU+/8VnnzxxRdm6NChJjIy0rRu3do89NBDVlfAn34uLp4+1+rk5+ebO+64w8TFxZmYmBhz2223VWre4XQ6zYwZM0xiYqKJiooy11xzjfn666+t495+55s3bzaSzL333usWgzefVXXvKz8/37Rv3960aNHCREREWLl/ww03eH0NTw1cfvreNm7caHr37m0iIiJM586dzV//+tdK5+fm5pobb7zRNG/e3MTGxprrr7/eakwCIDjZjPHzgvkGwGazac+ePerQoYP+8Ic/6IEHHrD+S2xZWZny8/NVWFho3ZO0d+9epaSkeLy34L333tPdd99t3djpyfbt29W9e3cVFRUpIiKift4UAJwBdu/erfPOO0/PPfeczj77bNlsNh08eFD33HOPRo0apQULFgQ6RATAr3/9ax05ckT33nuvmjRposLCQr3xxht66qmndPjwYeteNACorTNqGZ4nbdu21UUXXaRXXnlFUvkNnHl5eV53r3v11Vfduuv84he/0L333qu+fftKKr8nqlWrVhRKAHCaUlJSdNddd2nu3Ln65ptvVFJSotatWystLU0zZswIdHgIkMmTJ+uBBx7QddddJ4fDoejoaHXr1k0vvfQShRKA03LGzywdPXpUXbp00RNPPKGLL75YL730kp544gkdOHDAag9a3cxSu3bt9MILL2jgwIHWvoceekhvv/22Fi5cqNzcXN16662aNGmSZs+e7bf3CAAAAOD0nPEzS7GxsVqxYoWmTJmi7OxsnXvuuVqxYkWl5yhU5csvv9Q333zj1s1q5syZ2rdvn4YMGaIWLVrojjvu0MyZM+vrLQAAAACoB2fkzBIAAAAA1OSMes4SAAAAAHiLYgkAAAAAPDgj7lkqKyvTN998o2bNmslmswU6HAAAAAABYoyxHlAdElL93NEZUSx98803Sk5ODnQYAAAAABqI/fv3q23bttWec0YUS82aNZNU/oHExMQENBan06l3331XaWlpXj/LCZDIHfiGvIEvyBv4ityBL/ydNw6HQ8nJyVaNUJ0zolhyLb2LiYlpEMVSdHS0YmJi+EcEtULuwBfkDXxB3sBX5A58Eai88eb2nIA1eDh8+LBSUlK0d+/eWo0bPXq07rzzzvoJCgAAAABOCsjM0qFDhzR8+PBaF0rvvPOO1q5dqy+++KJ+AgMAAACAkwIyszR69GiNHj26VmMKCws1adIkzZ8/X7GxsfUTGAAAAACcFJCZpYyMDHXs2FFTp071eszDDz+swsJChYWFae3atRo4cGCV6wyLi4tVXFxsbTscDknl6yGdTqfHMcYYlZaWqrS0VMYY799MLZWUlCgsLEzHjh1TWNgZcctYQNhsNoWGhio0NLTRtIt35W5VOQx4Qt7AF+QNfEXuwBf+zpvaXMdm6rMyqOniNpv27NmjDh06VHve119/rc6dO6t3795KS0vT8uXL1a5dO73xxhsefxGeO3eu5s2b57b/5ZdfVnR0tNv+kJAQxcbGKioqqtH8Yo3yArigoEB5eXkqKysLdDgAAABoAAoKCjR27Fjl5eXV2PwtKIqlhx56SIsWLdIXX3yhiIgI5efnq3379nrllVeUlpbmdr6nmaXk5GQdOnTI7QMpKyvTnj17FBoaqsTERNnt9notmIwxOn78uJo0aUJhVo+MMXI6ncrNzVVpaalSUlJqfOhYQ+d0OrVmzRoNGTKEDkPwGnkDX5A38BW5A1/4O28cDocSEhK8KpaCYh3YgQMHdPnllysiIkJS+XOTOnXqpD179ng8PyIiwjr3VHa73e0LKCoqkjFGSUlJHmed6lpZWZmcTqeioqKC/pf3YBAeHq59+/bJGNNo/tH2lMdATcgb+IK8ga/IHfjCX3lTm2sExW/rycnJKiwstLbLysp04MABtW/fvs6uQeHSOPG9AgAAwFcNambJ4XAoKirKrdq7/vrr1bNnT73++uvq06ePnnrqKRUXF+uSSy4JUKQAAAAAGrsG9Z/du3XrplWrVrntP+ecc/TPf/5TjzzyiDp16qRVq1bpP//5j5o1axaAKAEAAACcCQJaLBljKjV32Lt3r0aOHOnx3KuuukqfffaZCgsLlZ2dfcbPKi1evFjdu3f3eGzu3Lmy2Wyy2Wxq0qSJLr30UmVmZtZrPBs2bFCXLl2UkJCgBQsWeD3utddeU/v27dWmTRstW7bM62OStHnzZp1zzjmnHTsAAADgSYOaWULdGTZsmI4cOaIdO3aoS5cuuvbaa+vtWrm5uRoxYoTGjBmjzZs3a+nSpVq3bl2N47Kzs/WrX/1Ks2fP1jvvvKM5c+Zo165dNR6TpG3btmnUqFGVuh4CAAAAdYliyQNjjApOlNTbT+GJUo/767KLu91uV2xsrDp27Kg5c+Zo//79OnToULVjLrzwQsXGxrr9rFixotpxS5cuVevWrTV79mx16tRJc+bM0aJFi2qM8dlnn9XAgQM1YcIEnX/++ZoyZYpefPHFGo8dP35co0aN0qRJk7z8NAAAAIDaa1ANHhqKQmepus55x+/XzXloqKLD6/YrMcbo1VdfVVxcnGJjY6s9d+XKlR6faNyiRYtqx23fvl2DBg2ynhvVu3dvzZw5s8bYtm/friuvvNLa7t27tx5++OEaj9ntdn300UfavXu3nnvuuRqvAwAAAPiCYqmRWrVqlWJjY1VUVKSEhAS99NJLCgur/utOSkry6VoOh0Ndu3a1tmNiYnTw4EGvxqWkpHgcV92x8PBwJSUlaffu3T7FCwAAAHiDYsmDKHuoch4aWi+vXVZWpnxHvprFNHN7BlCUPbTOrjNw4EBlZGRo4sSJSklJ0bBhw+rstX8qLCys0kOAIyMjVVBQcFrjfH1NAAAAoK5QLHlgs9nqfDmcS1lZmUrCQxUdHlavD0yNjo5Whw4dNGXKFI0dO1bp6elq0qRJtWMuvPBCffXVV277lyxZohEjRlQ5Lj4+Xrm5udZ2fn6+wsPDa4yxunG+viYAAAAalrKiIh1bv0G2cLuaDRoU6HBqhQYPjdywYcMUHx/vsfX2T61cuVJZWVluP4MHD652XK9evbRlyxZrOysry6slfdWN8/U1AQAA0LCUHjmig1On6uDUuwMdSq1RLAUxp9OpAwcOVPo5ceJEpXNCQkJ02223KSMjo8bXS0pKUocOHdx+oqOjqx03YsQIbdq0SevWrVNJSYnS09M1dGjFMsajR4+qtLTUbdx1112nV155RTk5OTp+/Lieeuopa1x1xwAAABA8TElJ+R9quH++IaJYCmI5OTlKTk6u9LNt2za388aPH6/t27crKyurXuJISEjQ448/rqFDh6p169bKzs7WrFmzrONxcXHasWOH27gLLrhAU6ZMUY8ePdS2bVsZY6x24NUdAwAAQPBwFUu2ICyWgi9iSJJuueUW3XLLLR6P9e3bt9J2y5Yt6/3hrZMmTVJaWpp27typAQMGKCYmxjpW3fOjHnvsMY0ZM0YHDx7UoEGDKjV1qO6YJF122WXau3dvnb8XAAAA1CFXsRRad83M/IViCXUmNTVVqamptR7XrVs3devWrdbHAAAA0PAZ1+0YYcFXLLEMDwAAAEC9MSXlxZItzB7gSGqPYgkAAABA/SlxSgrOZXgUSwAAAADqjWsZXjA2eKBYAgAAAFBvjNPVOpyZJQAAAACwmFJX63DuWQIAAACACkHcOpxiCQAAAEC9oXU4/G7x4sXq3r27x2Nz586VzWaTzWZTkyZNdOmllyozM7Ne49mwYYO6dOmihIQELViwwOtxr732mtq3b682bdpo2bJlbsc3b96sc845py5DBQAAgB+ZEpbhoYEZNmyYjhw5oh07dqhLly669tpr6+1aubm5GjFihMaMGaPNmzdr6dKlWrduXY3jsrOz9atf/UqzZ8/WO++8ozlz5mjXrl3W8W3btmnUqFEqLi6ut9gBAABQz1iG18gYI504Xn8/zgLP+42ps7dgt9sVGxurjh07as6cOdq/f78OHTpU7ZgLL7xQsbGxbj8rVqyodtzSpUvVunVrzZ49W506ddKcOXO0aNGiGmN89tlnNXDgQE2YMEHnn3++pkyZohdffFGSdPz4cY0aNUqTJk3y/k0DAACgwQnm1uHBF7E/OAukR9vUy0uHSIqt6uD930jhTer0esYYvfrqq4qLi1NsbJVXliStXLlSTqfTbX+LFi2qHbd9+3YNGjRINptNktS7d2/NnDmzxti2b9+uK6+80tru3bu3Hn74YUnlxd5HH32k3bt367nnnqvxtQAAANAwBXPrcIqlRmrVqlWKjY1VUVGREhIS9NJLLymshmo+KSnJp2s5HA517drV2o6JidHBgwe9GpeSkuJxXHh4uJKSkrR7926fYgIAAEDDYLUODw2+0iP4IvYHe3T5LE89KCsrkyM/XzHNmikk5CerIO3RdXadgQMHKiMjQxMnTlRKSoqGDRtWZ6/9U2FhYYqIiLC2IyMjVVBQUG/jAAAAEESCeBke9yx5YrOVL4errx97tOf9J5ex1YXo6Gh16NBBU6ZM0dKlS3X8+PEax/h6z1J8fLxyc3Ot7fz8fIWHh9d4PV/HAQAAIHiwDA8N1rBhwxQfH69ly5ZpwoQJ1Z7r6z1LvXr1qtT2Oysry6slfb169dKWLVs0fvz4Wo0DAABA8LCW4dE6HP7kdDp14MCBSj8nTpyodE5ISIhuu+02ZWRk1Ph6SUlJ6tChg9tPdHT1ywNHjBihTZs2ad26dSopKVF6erqGDh1qHT969KhKXQ8jO8V1112nV155RTk5OTp+/LieeuqpSuMAAADQCNA6HIGQk5Oj5OTkSj/btm1zO2/8+PHavn27srKy6iWOhIQEPf744xo6dKhat26t7OxszZo1yzoeFxenHTt2uI274IILNGXKFPXo0UNt27aVMYZW4QAAAI2MKTl5z5I9+Ba1BV/EkCTdcsstuuWWWzwe69u3b6Xtli1b1vuDXSdNmqS0tDTt3LlTAwYMUExMjHXMVPP8qMcee0xjxozRwYMHNWjQoEoNHyTpsssu0969e+srbAAAANQzc3JmSUE4s0SxhDqTmpqq1NTUWo/r1q2bunXrVg8RAQAAINCCuXU4y/AAAAAA1J8SWocDAAAAgBtrGV4Qtg6nWAIAAABQb2gdDgAAAACe0DocAAAAANy5WoezDA8AAAAATsEyPAAAAADwhGV48LfFixere/fuHo/NnTtXNptNNptNTZo00aWXXqrMzMx6jWfDhg3q0qWLEhIStGDBglqN3bx5s84555x6igwAAACB5FqGZ7PTOhwNxLBhw3TkyBHt2LFDXbp00bXXXltv18rNzdWIESM0ZswYbd68WUuXLtW6deu8Grtt2zaNGjVKxcXF9RYfAAAAAsdqHc7MUuNgjFGBs6DefgpLCj3uN8bU2Xuw2+2KjY1Vx44dNWfOHO3fv1+HDh2qdsyFF16o2NhYt58VK1ZUO27p0qVq3bq1Zs+erU6dOmnOnDlatGhRjTEeP35co0aN0qRJk2r13gAAABA8gvmepeCbC/ODwpJC9Xm5j9+v+/HYjxVtj67T1zTG6NVXX1VcXJxiY2OrPXflypVyOp1u+1u0aFHtuO3bt2vQoEGy2WySpN69e2vmzJk1xma32/XRRx9p9+7deu6552o8HwAAAEHI6SqWgm9miWKpkVq1apViY2NVVFSkhIQEvfTSSwoLq/7rTkpK8ulaDodDXbt2tbZjYmJ08ODBGseFh4crKSlJu3fv9um6AAAAaPhM6cnW4UG4DI9iyYOosCh9PPbjenntsrIy5efnq1mzZgoJqbwKMiosqs6uM3DgQGVkZGjixIlKSUnRsGHD6uy1fyosLEwRERHWdmRkpAoKCurtegAAAAgewbwML2D3LB0+fFgpKSnau3dvrcY5nU6df/75Wr9+fb3EJUk2m03R9uh6+4kKi/K437WMrS5ER0erQ4cOmjJlipYuXarjx4/XOMbXe5bi4+OVm5trbefn5ys8PPy03wMAAAAaAZbh1c6hQ4c0fPjwWhdKkvTHP/5R2dnZdR9UIzVs2DDFx8dr2bJlmjBhQrXn+nrPUq9evbRs2TJrOysry+clfQAAAGhcXMvwbDXcEtIQBWRmafTo0Ro9enStx+3evVvp6enq0KFD3QcVhJxOpw4cOFDp58SJE5XOCQkJ0W233aaMjIwaXy8pKUkdOnRw+4mOrr7pxIgRI7Rp0yatW7dOJSUlSk9P19ChQ63jR48eValrrSoAAADOKMHcOjwg5V1GRoY6duyoqVOn1mrc7bffrhkzZujtt9+u9rzi4uJKz+1xOBySyouLn86cOJ1OGWNUVlamsrKyWsXjC1d7cNc1fVVWVqacnBwlJydX2v/hhx/KGFPp9ceNG6d58+Zp27ZtVT7I9nTEx8dbBVLz5s3VpEkTPfPMM9b14+Li9Omnn1Z5bdd59fH5l5WVyRgjp9Op0CD8C3oqV+56mv0DqkLewBfkDXxF7sATU1KeD6XynBv+zpvaXMdm6vLhPrVks9m0Z88er2aKnn/+ef3lL3/Rxx9/rMGDB2vu3Lm67LLLPJ47d+5czZs3z23/yy+/7DZLEhYWplatWik5OZn7bE7TV199pV27dumSSy5RTExMoMORJJ04cUL79+/Xd999pxLXf9UAAACA37T/858V8d332n/rBBWmpgY6HBUUFGjs2LHKy8ur8XfWoFg4mJubq5kzZ2r16tU1tr+WpJkzZ2ratGnWtsPhUHJystLS0tw+kKKiIu3fv19NmzZVZGRkncf+U8YYqxteXTZ0aAi6d+9eLzNXp6OoqEhRUVHq37+/X77f+uR0OrVmzRoNGTJEdnvwdZNBYJA38AV5A1+RO/Bk39//Iaekvhf3U1Svi9yO+ztvXKvOvBEUxdLUqVM1fvx4r38Rj4iIqNTK2sVut7t9AaWlpbLZbAoJCXFr5V0fXEvNXNdE/QoJCZHNZvP43QerxvRe4D/kDXxB3sBX5A4qKSu/dz0sMrLavPBX3tTmGkHx2/rLL7+sp556ymplvWnTJl199dWaP39+oEMDAAAAUB1ah9cNh8OhqKgot2pvz549lbZHjx6tqVOn6oorrvBneAAAAABqidbhdaRbt25atWqV2/6ftrKOjIxUq1atFBsb6/8gAQAAAHitonV48BVLAY34p434vH1I7fr16+s+GAAAAAB1ryR4l+E1qJklAAAAAI0Ly/AAAAAAwINgXoZHsRSkFi9eXGUr9blz58pms8lms6lJkya69NJLlZmZWa/xbNiwQV26dFFCQoIWLFjg9bjzzz/fitVms2nChAn1GCUAAAD8zZpZslMsoYEYNmyYjhw5oh07dqhLly669tpr6+1aubm5GjFihMaMGaPNmzdr6dKlWrduXY3jCgoK9NVXX+mHH37QkSNHdOTIET311FP1FicAAAD8yxgjOZ2SJFto8N2zFHzlnR8YY2QKC+vltcvKylRWWKiysDDpJw+ltUVFyWaz1cl17Ha79VyqOXPm6JlnntGhQ4eUkJBQ5ZgLL7xQX331ldv+JUuWaMSIEVWOW7p0qVq3bq3Zs2fLZrNpzpw5WrRokQYOHFhtjNu2bVO3bt2UmJjo/RsDAABA8Cgrq/gzxVLjYAoLtevCnvV6je897Dtn26eyRUfX6XWMMXr11VcVFxdXY6v1lStXynmy8j9VixYtqh23fft2DRo0yCr0evfurZkzZ9YY2yeffKIDBw4oMTFRTqdTY8aM0cKFCxUREVHjWAAAADR81v1Kkmw/eZZqMKBYaqRWrVql2NhYFRUVKSEhQS+99JLCauhAkpSU5NO1HA6Hunbtam3HxMTo4MGDNY773//+p8suu0xz587VkSNHNHr0aC1cuFC/+93vfIoDAAAADcypxRIzS42DLSpK52z7tF5eu6ysTI78fMU0a6YQD8vw6srAgQOVkZGhiRMnKiUlRcOGDauz1/6psLCwSrNBkZGRKigoqHHc3/72t0rbs2fP1l/+8heKJQAAgEbC1dxBCs7W4cEXsR/YbLY6Xw5nKStTSEmJQqKj3YqluhQdHa0OHTpoypQpGjt2rNLT09WkSZNqx/h6z1J8fLxyc3Ot7fz8fIWHh9c65tjYWB04cKDW4wAAANAwnboMj3uW0OAMGzZM8fHxWrZsWY1tuX29Z6lXr15atmyZtZ2VleXVkr4+ffpo+fLlatOmjSRp69at6tChQ43jAAAAEBysYikkRLZ6nCioL8EXMSxOp1MHDhyo9HPixIlK54SEhOi2225TRkZGja+XlJSkDh06uP1E1zDLNmLECG3atEnr1q1TSUmJ0tPTNXToUOv40aNHVXrKFKzLueeeqzvuuEOffvqpli5dqieeeEKTJk3y8t0DAACgwTtZLAXjEjyJYimo5eTkKDk5udLPtm3b3M4bP368tm/frqysrHqJIyEhQY8//riGDh2q1q1bKzs7W7NmzbKOx8XFaceOHW7jFixYoJCQEA0YMECPPPKI/vjHP+rXv/51vcQIAAAA/7PuWQrSYik4o4ZuueUW3XLLLR6P9e3bt9J2y5YtVVxcXK/xTJo0SWlpadq5c6cGDBigmJgY65gxxuOY2NhYLV++vF7jAgAAQOCYIJ9ZCs6o0SClpqYqNTU10GEAAACgoXAVS0HY3EFiGR4AAACAeuJahhesM0sUSwAAAADqhXGe7IZHsRTcqrqvBsGN7xUAACCASlmGF9TsdrskqaCgIMCRoD64vlfX9wwAAAD/ocFDkAsNDVVsbKx++OEHSVJ0dLRsNlu9Xa+srEwnTpxQUVGRQoLwwVzBwhijgoIC/fDDD4qNjVVokP7XDAAAgGBmSlytw4Pzd7EzvliSpFatWkmSVTDVJ2OMCgsLFRUVVa9FGcrFxsZa3y8AAAD8y7iW4YUF5yofiiVJNptNrVu3VosWLeR0Ouv1Wk6nUxs3blT//v1ZGlbP7HY7M0oAAACBFOStwymWThEaGlrvv1yHhoaqpKREkZGRFEsAAABo1Fytw4N1GR43zQAAAACoF67W4cG6DI9iCQAAAED9oHU4AAAAALhzLcML1tbhFEsAAAAA6oVrGR73LAEAAADAKYK9dTjFEgAAAID6EeStwymWAAAAANQLU0LrcAAAAABwY0pYhgcAAAAA7mgdDgAAAADuXMvwbHZahwMAAACAxbUMT8wsAQAAAEAFq3V4KDNLAAAAAFDBavBAsQQAAAAAFlqHAwAAAIAH1jI8WocDAAAAwClKaB0OAAAAAG5oHQ4AAAAAHlS0DqdYAgAAAIAKpSzDAwAAAAA3xnmyWGIZHgAAAABUMKUnW4czs1Q7hw8fVkpKivbu3evV+RkZGWrdurXsdrvS0tL07bff1m+AAAAAAE4LrcN9cOjQIV199dVeF0qbNm3S7Nmz9eKLL2rPnj0qKirSvffeW79BAgAAADg9rmV4PJTWe6NHj9bo0aO9Pn/Xrl16+umnNXjwYLVt21bjxo1TZmZmPUYIAAAA4HQF+zK8gNxplZGRoY4dO2rq1KlenT9+/PhK27t27VJqamo9RAYAAACgrrhahwfrMryAFEsdO3b0eezhw4f1j3/8Qy+99FKV5xQXF6u4uNjadjgckiSn0ymn0+nzteuC6/qBjgPBh9yBL8gb+IK8ga/IHfxU2clcKFPVeeHvvKnNdWzGGFOPsVR/cZtNe/bsUYcOHbwec8MNN+jYsWNatWpVlefMnTtX8+bNc9v/8ssvKzo62pdQAQAAANRS8t+eVtS+fTp40691/NxzAx2OJKmgoEBjx45VXl6eYmJiqj03qIql5557Tg888ICysrLUsmXLKs/zNLOUnJysQ4cO1fiB1Den06k1a9ZoyJAhstuDczoSgUHuwBfkDXxB3sBX5A5+av+YsSrOzlbrvzylJgMGeDzH33njcDiUkJDgVbEUNE+H+uSTTzR16lStXLmy2kJJkiIiIhQREeG23263N5i/uA0pFgQXcge+IG/gC/IGviJ3YCkrb/AQFhFZY074K29qc40G9VBah8PhcQ3h999/r+HDh+t3v/udevbsqWPHjunYsWMBiBAAAACA12gdXne6devm8V6kZcuW6YcfftCsWbPUrFkz6wcAAABAw0Xr8NPw09ulqnpI7dSpU71uMw4AAACgYQj21uENamYJAAAAQCNSwjI8AAAAAHDjWoZnCwuavnKVUCwBAAAAqBeuZXgKpVgCAAAAgAoswwMAAAAAdxUNHphZAgAAAABLRetwiiUAAAAAsFgNHuwUSwAAAAAg6eQzVZ1OSZItSB9KS7EEAAAAoO6VlVX8mWIJAAAAAMpZbcMl2ez2AEbiO4olAAAAAHXv1GKJmSUAAAAAKFdpZonW4QAAAABQzmobLkkUSwAAAABQzppZCg2VzWYLbDA+olgCAAAAUPdOFkvBer+SRLEEAAAAoB5Yy/CCdAmeRLEEAAAAoB4Y58mZJYolAAAAADhFKcvwAAAAAMCNaxkeM0sAAAAAcArXMjzuWQIAAACAU7EMDwAAAADcuZ6zxDI8AAAAADiFKXG1DmdmCQAAAAAsFTNL9gBH4juKJQAAAAB1j3uWAAAAAMAdrcMBAAAAwANahwMAAACAJyzDAwAAAAB3tA4HAAAAAA9oHQ4AAAAAHphSWocDAAAAgLsS7lkCAAAAADcswwMAAAAADyoaPLAMDwAAAAAq0DocAAAAANxZM0t2WocDAAAAgMW6Z4mZJQAAAACoQOtwAAAAAPCE1uEAAAAA4I7W4QAAAADgAa3DAQAAAMATWocDAAAAgDvXMjxahwMAAADAKVzL8BRKsVRrhw8fVkpKivbu3evV+Rs2bFCXLl2UkJCgBQsW1G9wAAAAAE4Py/B8c+jQIV199dVeF0q5ubkaMWKExowZo82bN2vp0qVat25d/QYJAAAAwGfGebJYYhle7YwePVqjR4/2+vylS5eqdevWmj17tjp16qQ5c+Zo0aJF9RghAAAAgNNhSk+2Dg/imaWAlHkZGRnq2LGjpk6d6tX527dv16BBg2Sz2SRJvXv31syZM6s8v7i4WMXFxda2w+GQJDmdTjmdTt8DrwOu6wc6DgQfcge+IG/gC/IGviJ3cKqyEyfK/9cWUm1O+DtvanOdgBRLHTt2rNX5DodDXbt2tbZjYmJ08ODBKs9/7LHHNG/ePLf97777rqKjo2t17fqyZs2aQIeAIEXuwBfkDXxB3sBX5A4kqc2336qppB05/5XjrZp/B/dX3hQUFHh9blAsIAwLC1NERIS1HRkZWe2bnDlzpqZNm2ZtOxwOJScnKy0tTTExMfUaa02cTqfWrFmjIUOGyG4P3gd0wf/IHfiCvIEvyBv4itzBqb5ZsUIFkrpdeKFihg2r8jx/541r1Zk3gqJYio+PV25urrWdn5+v8PDwKs+PiIioVFy52O32BvMXtyHFguBC7sAX5A18Qd7AV+QOJEmlZZKksPAIr/LBX3lTm2sExXOWevXqpS1btljbWVlZSkpKCmBEAAAAAKp18jlLtrDgbfDQoIolh8Ph8YarESNGaNOmTVq3bp1KSkqUnp6uoUOHBiBCAAAAAN4wVrEUFIvZPGpQxVK3bt20atUqt/0JCQl6/PHHNXToULVu3VrZ2dmaNWtWACIEAAAA4A1ah58mY0yl7eoeUjtp0iSlpaVp586dGjBgQMAbNQAAAAComil1zSwF7/1rQTUnlpqaqtTU1ECHAQAAAKAmTu5ZAgAAAAA3jWEZHsUSAAAAgDpX0eAheJfhUSwBAAAAqHu0DgcAAAAAd7QOBwAAAAAPKu5ZolgCAAAAgAoswwMAAAAAdyzDAwAAAAAPWIYHAAAAAB5YM0t2iiUAAAAAkCQZYyruWeKhtAAAAABwUlmZ9UfuWQIAAACAk1xL8CRJFEsAAAAAcNIpxRLL8AAAAADgpFNnlliGBwAAAAAnWW3DJZbhAQAAAICLcZ6cWQoNlc1mC2wwp4FiCQAAAEDdKg3+tuESxRIAAACAOmYtwwviJXgSxRIAAACAOuZahhfMzR0kiiUAAAAAdY1leAAAAADgztU6nJklAAAAADiFKeGeJQAAAABwV8rMEgAAAAC4sZbhcc8SAAAAAFSoWIZHsQQAAAAAlooGD/YAR3J6KJYAAAAA1C1ahwMAAACAO1qHAwAAAIAHtA4HAAAAAE9YhgcAAAAA7liGBwAAAAAe0DocAAAAADwwJU5JtA4HAAAAgMpKy2eWuGcJAAAAAE7hWoZns3PPEgAAAABYXA0eFEqxBAAAAAAVaB0OAAAAAO6s1uEswwMAAACAClbrcGaWAAAAAKACrcMBAAAAwBNahwMAAACAO2sZXtgZWCw5nU4988wzkqTc3FzddddduvPOO/Xdd995NT47O1u9evVSXFycpk+fLmNMjWP+9Kc/qWXLloqJidF1112nw4cP+xI6AAAAgHpmNXg4E5fh3XzzzXr22WclSVOmTFFOTo527dqlm2++ucaxxcXFGj58uHr27KnMzEzl5ORo8eLF1Y7ZuHGjXnjhBW3cuFHbtm1TUVGR7rnnHl9CBwAAAFDfGknrcJ96+b311lvatm2bnE6nVq9era+//lr5+fn62c9+VuPYt99+W3l5eVqwYIGio6P16KOPavLkyRo3blyVYz755BMNGzZM55xzjiRpzJgx+tvf/uZL6AAAAADqmXE2jtbhPkUfHR2tb7/9Vnv27FGnTp3UvHlz/fe//1Xz5s1rHLt9+3b17dtX0dHRkqRu3bopJyen2jHnnXeepkyZottvv13NmjXTokWLNGTIkCrPLy4uVnFxsbXtcDgklS8fdDqd3rzFeuO6fqDjQPAhd+AL8ga+IG/gK3IHLqUnc6BMthrzwd95U5vr+FQsTZs2TZdddplsNpueffZZffbZZ7r22ms1ceLEGsc6HA6lpKRY2zabTaGhoTpy5Iji4uI8jrniiivUqVMnpaamSpJ69eqlGTNmVHmNxx57TPPmzXPb/+6771pFWqCtWbMm0CEgSJE78AV5A1+QN/AVuYNWX+9TjKTP/7dbR956y6sx/sqbgoICr8/1qVi69957NXz4cEVGRqp9+/Y6ePCgXnzxxWpne6wLhoUpIiKi0r7IyEgVFBRUWSy9+uqr2rdvnz7//HMlJibq3nvv1Y033qjXX3/d4/kzZ87UtGnTrG2Hw6Hk5GSlpaUpJiamFu+07jmdTq1Zs0ZDhgyR3R7cN7zBv8gd+IK8gS/IG/iK3IHLd+vX65ikLuedp9hhw6o9199541p15g2fFxG67h+SpKSkJCUlJXk1Lj4+XtnZ2ZX25efnKzw8vMoxy5Yt0x133GFdc+HChWrevLmOHj2q2NhYt/MjIiLcCjJJstvtDeYvbkOKBcGF3IEvyBv4gryBr8gd2MrKu12Hhod7nQv+ypvaXMOnbng//vijHnjgAUnSl19+qWuuuUbDhw/Xzp07axzbq1cvbdmyxdreu3eviouLFR8fX+WYkpISff/999b2t99+K0kqPfmwKwAAAAANR2NpHe7TzNKNN95oVWRTpkxRYmKiQkJCNH78eH300UfVju3fv7/y8vK0ZMkS3XTTTZo/f74GDx6s0NBQORwORUVFuVV7l1xyiRYsWKC2bdsqKipKCxcu1MUXX6yzzjrLl/ABAAAA1CerWDoDW4dv3LhRO3fuVFFRkTZt2qQffvhBR48etRowVHvBsDBlZGRo7Nixmj59ukpLS7VhwwZJ5Z3xFi5cqJEjR1YaM3XqVH3zzTd6+OGHdejQIV188cVatGiRL6EDAAAAqGcVM0tnYOvwxMREbdmyRUVFRbrgggsUFRWljRs3qmXLll6NHzlypHbv3q3MzEz169dPiYmJksqX5HkSGRmpJ598Uk8++aQv4QIAAADwI+O6XSb0DCyWHn74Yf3qV79SeHi4/vWvf2nz5s0aNWqUFixY4PVr1KYpBAAAAIAgciYvw7vxxhs1atQohYaGKjIyUj/++KOysrLUuXPnuo4PAAAAQJBpLMvwfOqGJ0lNmjSRw+HQp59+qtLSUgolAAAAAJJOXYYX3DNLPhVLeXl5GjVqlFq1aqWf//znatWqlX7xi1/U6gFPAAAAABqnxtI63KdiafLkySorK9PBgwdVWFior7/+Wk6nU5MmTarr+AAAAAAEmzP5nqW3335bn376qVq3bi2pvFnDwoUL1bNnzzoNDgAAAEDwcc0snZHL8Nq1a6e1a9dW2rd27Vq1b9++ToICAAAAELxc9ywF+zI8n2aWnnjiCV111VV69dVX1bFjR3311Vf66KOPtGrVqrqODwAAAECwaSTL8HyaWerfv7927typyy67TDabTQMHDtR///tfRURE1HV8AAAAAIJMY2kd7nP0bdu21YwZM6ztgwcP6uKLL1apq00gAAAAgDNSRevw4C6WfH7OkifGmLp8OQAAAABByJpZslMsWWw2W12+HAAAAIBg5CqWzsRueAAAAABQlcayDM/r6Hv06FHtzNGJEyfqJCAAAAAAwa2xLMPzOvqpU6fWYxgAAAAAGgNjTKNZhud1sXTzzTfXZxwAAAAAGoNTumMHe+tw7lkCAAAAUGfMqY8SolgCAAAAgHLGWWL9OdiX4VEsAQAAAKg7pacUS8wsAQAAAEA5luEBAAAAgAfWMrzQ0GofPRQMKJYAAAAA1J3SxtE2XKJYAgAAAFCHrAfSBvkSPIliCQAAAEAdMiUn71miWAIAAACAU7AMDwAAAADcsQwPAAAAADxgGR4AAAAAeGBKnJKYWQIAAACAyk4+lJZ7lgAAAADgFK57lhRGsQQAAAAAFtc9S7Ywe4AjOX0USwAAAADqDq3DAQAAAMAdrcMBAAAAwANahwMAAACAB7QOBwAAAABPaB0OAAAAAO4qluFRLAEAAACApWIZHq3DAQAAAKACy/AAAAAAwJ1xnmwdbqfBAwAAAABYzMmZJYVSLAEAAACAxbpniWV4AAAAAHAK1z1LLMPzTXZ2tnr16qW4uDhNnz5dxhivx44ePVp33nlnPUYHAAAAwFdW63BmlmqvuLhYw4cPV8+ePZWZmamcnBwtXrzYq7HvvPOO1q5dq4cffrh+gwQAAADgE1qHn4a3335beXl5WrBggc4++2w9+uijWrRoUY3jCgsLNWnSJM2fP1+xsbH1HygAAACA2mtErcP9vpBw+/bt6tu3r6KjoyVJ3bp1U05OTo3jHn74YRUWFiosLExr167VwIEDZbPZPJ5bXFys4uJia9vhcEiSnE6nnE5nHbwL37muH+g4EHzIHfiCvIEvyBv4ityBJJUWn5AklYWEeJUL/s6b2lzHZmpzw1AduOeee1RUVKS//vWv1r7ExER98cUXiouL8zjm66+/VufOndW7d2+lpaVp+fLlateund544w2PBdPcuXM1b948t/0vv/yyVaQBAAAAqHuJK1Yo7sOPdHjgQB2+Ymigw3FTUFCgsWPHKi8vTzExMdWe6/eZpbCwMEVERFTaFxkZqYKCgiqLpcWLF6tly5Zas2aNIiIidNddd6l9+/Zas2aN0tLS3M6fOXOmpk2bZm07HA4lJycrLS2txg+kvjmdTq1Zs0ZDhgyR3R786zjhP+QOfEHewBfkDXxF7kCScrd9pjxJqed0Vp9hw2o8399541p15g2/F0vx8fHKzs6utC8/P1/h4eFVjjlw4IAuv/xyq8hq1qyZOnXqpD179ng8PyIiwq0gkyS73d5g/uI2pFgQXMgd+IK8gS/IG/iK3Dmz2crKJElhERG1ygN/5U1truH3Bg+9evXSli1brO29e/equLhY8fHxVY5JTk5WYWGhtV1WVqYDBw6offv29RorAAAAgNoxpa7W4Txnqdb69++vvLw8LVmyRJI0f/58DR48WKGhoXI4HB5vuLr++uu1cuVKvf766zpw4IBmzpyp4uJiXXLJJf4OHwAAAEA1KlqHUyzVWlhYmDIyMjRx4kS1bNlSr732mubPny+pvDPeqlWr3Macc845+uc//6lHHnlEnTp10qpVq/Sf//xHzZo183f4AAAAAKpz8qG0tjBah/tk5MiR2r17tzIzM9WvXz8lJiZKKl+SV5WrrrpKV111lZ8iBAAAAOALU1JS/gees+S7pKQkJSUlBeryAAAAAOqB654lW1jwN/nw+zI8AAAAAI3YyZmlxrAMj2IJAAAAQJ0xVrFEgwcAAAAAsNA6HAAAAAA8qGgdzjI8AAAAAKhgtQ5nZgkAAAAALBXL8JhZAgAAAABLRYMHWocDAAAAQAVahwMAAACAO1qHAwAAAIAHtA4HAAAAAA9oHQ4AAAAAntA6HAAAAADcsQwPAAAAADywGjzYKZYAAAAAoIKrWOKhtAAAAABQwTWzxDI8AAAAADiF654lluEBAAAAwEnGGJbhAQAAAIAbVyc80TocAAAAACzmlGJJFEsAAAAAUM44S6w/M7MEAAAAAC6lpxRL3LMEAAAAAOWstuESy/AAAAAAwMWUnLxnKTRUNpstsMHUAYolAAAAAHWjtPG0DZcolgAAAADUEdcyvMbQ3EGiWAIAAABQR6xleBRLAAAAAFDBlDglsQwPAAAAACo7+VBaluEBAAAAwClYhgcAAAAAHljL8CiWAAAAAOAUrmV43LMEAAAAABWs1uF2ZpYAAAAAwGLdsxRKsQQAAAAAFlqHAwAAAIAntA4HAAAAAHe0DgcAAAAAD2gdDgAAAACe0DocAAAAANwZZ3nrcIVRLAEAAACAxZSefM5SmD3AkdQNiiUAAAAAdYNleAAAAADgzrUMz2anwYPPsrOz1atXL8XFxWn69Okyxng91ul06vzzz9f69evrL0AAAAAAtWZOziwplGLJJ8XFxRo+fLh69uypzMxM5eTkaPHixV6P/+Mf/6js7Oz6CxAAAACATxpb63C/v4u3335beXl5WrBggaKjo/Xoo49q8uTJGjduXI1jd+/erfT0dHXo0KHa84qLi1VcXGxtOxwOSeWzUk6n87TiP12u6wc6DgQfcge+IG/gC/IGviJ3UHrihCTJhNi8zgN/501truP3Ymn79u3q27evoqOjJUndunVTTk6OV2Nvv/12zZgxQ2+//Xa15z322GOaN2+e2/53333Xum6grVmzJtAhIEiRO/AFeQNfkDfwFblz5jpr506dJenrgweV+dZbtRrrr7wpKCjw+ly/F0sOh0MpKSnWts1mU2hoqI4cOaK4uLgqxz3//PPKy8vTPffcU2OxNHPmTE2bNq3SNZOTk5WWlqaYmJjTfxOnwel0as2aNRoyZIjs9sbRUhH+Qe7AF+QNfEHewFfkDg7/70sd0ftq3/FsXTRsmFdj/J03rlVn3vB7sRQWFqaIiIhK+yIjI1VQUFBlsZSbm6uZM2dq9erVCvNi/WNERITbNSTJbrc3mL+4DSkWBBdyB74gb+AL8ga+InfOXCEqb9wW6kMO+CtvanMNvzd4iI+PV25ubqV9+fn5Cg8Pr3LM1KlTNX78eHXv3r2eowMAAADgK1qHn6ZevXppy5Yt1vbevXtVXFys+Pj4Kse8/PLLeuqppxQbG6vY2Fht2rRJV199tebPn++PkAEAAAB4obG1Dvf7u+jfv7/y8vK0ZMkS3XTTTZo/f74GDx6s0NBQORwORUVFuU2N7dmzp9L26NGjNXXqVF1xxRX+DB0AAABANazW4aGhAY6kbgTknqWMjAyNHTtW06dPV2lpqTZs2CCpvDPewoULNXLkyEpjftoqPDIyUq1atVJsbKx/ggYAAABQs5LymaXGsgwvIO9i5MiR2r17tzIzM9WvXz8lJiZKKl+S543169fXX3AAAAAAfMIyvDqSlJSkpKSkQF0eAAAAQB2zluF50cE6GPi9wQMAAACARsq1DC+scdyzRLEEAAAAoE6YkvLW4WokDR4olgAAAADUCdc9S7awxvFQYoolAAAAAHWi4p4lZpYAAAAAoIJ1zxINHgAAAADA0thah1MsAQAAAKgTtA4HAAAAAE9oHQ4AAAAA7mgdDgAAAAAe0DocAAAAADw5ObPEMjwAAAAAOIWxiiUaPAAAAACAhdbhAAAAAOBBRetwluEBAAAAQAWrdTgzSwAAAABgqWgdTrEEAAAAABardbidYgkAAAAAKri64fFQWgAAAACoQOtwAAAAAPDAah1OsQQAAAAA5YwxLMMDAAAAADeuWSWxDA8AAAAALOaUYolleAAAAABwknGWWH9mZgkAAAAAXEpPKZa4ZwkAAAAAyrnahktiGR4AAAAAuJiSk/cshYbKZrMFNpg6QrEEAAAA4PSVOCU1niV4EsUSAAAAgDrg6obXWJo7SBRLAAAAAOqAtQyPYgkAAAAAKhjXMjyKJQAAAAA4hWsZHvcsAQAAAEAFq3U4M0sAAAAAUMFVLLEMDwAAAABOxTI8AAAAAHBnzSzZmVkCAAAAAIvVOjyUYgkAAAAALFbrcJbhAQAAAMApXPcs0eABAAAAACoYJ63DAQAAAMCNKaV1OAAAAAC4o3V43cjOzlavXr0UFxen6dOnyxhT45iMjAy1bt1adrtdaWlp+vbbb/0QKQAAAABvWMvwaB3uu+LiYg0fPlw9e/ZUZmamcnJytHjx4mrHbNq0SbNnz9aLL76oPXv2qKioSPfee69/AgYAAABQI2sZHq3Dfff2228rLy9PCxYs0Nlnn61HH31UixYtqnbMrl279PTTT2vw4MFq27atxo0bp8zMTD9FDAAAAKAm1kNpG9EyPL+Xfdu3b1ffvn0VHR0tSerWrZtycnKqHTN+/PhK27t27VJqamqV5xcXF6u4uNjadjgckiSn0ymn0+lr6HXCdf1Ax4HgQ+7AF+QNfEHewFfkzpmt9MQJSZIJDa1VDvg7b2pzHb8XSw6HQykpKda2zWZTaGiojhw5ori4uBrHHz58WP/4xz/00ksvVXnOY489pnnz5rntf/fdd60iLdDWrFkT6BAQpMgd+IK8gS/IG/iK3Dkzxe7IVgtJ33z/nba99Vatx/srbwoKCrw+1+/FUlhYmCIiIirti4yMVEFBgVfF0qRJk9SvXz9dddVVVZ4zc+ZMTZs2zdp2OBxKTk5WWlqaYmJifA++DjidTq1Zs0ZDhgyR3W4PaCwILuQOfEHewBfkDXxF7pzZjnz7nQ5LSmrXXhcOG+b1OH/njWvVmTf8XizFx8crOzu70r78/HyFh4fXOPa5557Txo0blZWVVe15ERERbgWZJNnt9gbzF7chxYLgQu7AF+QNfEHewFfkzpkpROUdrkPDffv+/ZU3tbmG3xs89OrVS1u2bLG29+7dq+LiYsXHx1c77pNPPtHUqVP1yiuvqGXLlvUdJgAAAIBasFqHN6IGD34vlvr376+8vDwtWbJEkjR//nwNHjxYoaGhcjgcHm+4+v777zV8+HD97ne/U8+ePXXs2DEdO3bM36EDAAAAqILVOjys8cwq+r1YCgsLU0ZGhiZOnKiWLVvqtdde0/z58yWVd8ZbtWqV25hly5bphx9+0KxZs9SsWTPrBwAAAEADQevwujFy5Ejt3r1bmZmZ6tevnxITEyWVL8nzZOrUqZo6dar/AgQAAABQK6akVJJkszeeh9IG7J0kJSUpKSkpUJcHAAAAUIdMaXmxpNDGUyz5fRkeAAAAgMbHlJT3HrCFUSwBAAAAQAXXMrywxnPPEsUSAAAAgNNmSlytw5lZAgAAAABLRetwiiUAAAAAqMAyPAAAAABwZy3DY2YJAAAAACq4WofbuGcJAAAAACpUtA5nGR4AAAAAVLDuWWJmCQAAAAAstA4HAAAAAA9oHQ4AAAAAntA6HAAAAADcVSzDo1gCAAAAAIvVOjzMHuBI6g7FEgAAAIDTR+twAAAAAHBnaB0OAAAAAO5cy/BoHQ4AAAAApzCuZXh2iiUAAAAAqOBahkc3PAAAAACoUNE6nJklAAAAALBYrcNZhgcAAAAAp3CevGeJZXgAAAAAUKHiobTMLAEAAACAxWodTrEEAAAAAOWMMdLJBg8swwMAAAAAF9eskliGBwAAAAAWq224xDI8AAAAAHAxJcwsAQAAAIC7Eqf1R+5ZAgAAAICTzCn3LLEMDwAAAABOspbhhYbKZrMFNpg6RLEEAAAA4PScXIbXmJbgSRRLAAAAAE6TaxleY2ruIFEsAQAAADhNVutwiiUAAAAAqOAqlphZAgAAAIBTuZbhcc8SAAAAAFRgGR4AAAAAeGCKiyWxDA8AAAAALKVHj+q7R34vSbK3bh3gaOoWxRIAAAAAn5Tm5+vr8RNU/PnnCk1IUKu5cwMdUp2iWAIAAABQa6XHjmv/hFtV9N//KjQuTu2ff04RHVMCHVadolgCAAAAUCtlBQXaP/F2FW7frpDmzdXu+ecU0alToMOqcwEplrKzs9WrVy/FxcVp+vTpMsbUOGbDhg3q0qWLEhIStGDBAj9ECQAAAOCnyoqKtH/yZBVmfqqQpk3V7tlnFfmznwU6rHrh92KpuLhYw4cPV8+ePZWZmamcnBwtXry42jG5ubkaMWKExowZo82bN2vp0qVat26dfwIGAAAAIEkqO3FCB+78rQo2b5EtOlrJz2Qo6vzzAh1WvfF7b7+3335beXl5WrBggaKjo/Xoo49q8uTJGjduXJVjli5dqtatW2v27Nmy2WyaM2eOFi1apIEDB/ox8tNXVlqq7z9cJ/tnW/Wts0ChjeyhXahfpaWlsmf/l9xBrZA38AV5A1+RO42EMeUPmS0plSktkUpKyp+jVFqqE5s/0YktW6WICDV//FEVprRW4dHvvH7puGaJCgmi3PB7sbR9+3b17dtX0dHRkqRu3bopJyenxjGDBg2SzWaTJPXu3VszZ86s8vzi4mIVn+z1LkkOh0OS5HQ65XQ6T/ct+Ozw0e/0zhNT1W+n0XG9HrA4ELxSJHIHtUbewBfkDXxF7jR+J0KlP4xyasfX90pf127smmFv6azYVpX2uX4/99fv6bW5jt+LJYfDoZSUii4ZNptNoaGhOnLkiOLi4qoc07VrV2s7JiZGBw8erPIajz32mObNm+e2/91337WKtEAoOJGvb+Klz9sGLAQAAABAklRd14DSEJtKQ6TSUJX/78mfE2HS2u4h2tXW5tM1163foOjwZh6PrVmzxqfXrK2CggKvz/V7sRQWFqaIiIhK+yIjI1VQUFBlsfTTMa7zqzJz5kxNmzbN2nY4HEpOTlZaWppiYmJO8x34rqy0VD/8/OfatGmTfv7zn8seFjxTkAg8Z0kpuYNaI2/gC/IGviJ3zgzXnsZYT8vwnE6n1qxZoyFDhshut59ecF5wrTrzht+Lpfj4eGVnZ1fal5+fr/Dw8GrH5Obmen1+RESEW0EmSXa73S9fQJXsdrVKSFJ0eDO1SkgKbCwIOk6nk9xBrZE38AV5A1+ROzgd/vpdvTbX8Hs3vF69emnLli3W9t69e1VcXKz4+Hivx2RlZSkpKale4wQAAABwZvN7sdS/f3/l5eVpyZIlkqT58+dr8ODBCg0NlcPh8HjD1YgRI7Rp0yatW7dOJSUlSk9P19ChQ/0dOgAAAIAzSEDuWcrIyNDYsWM1ffp0lZaWasOGDZLKO+MtXLhQI0eOrDQmISFBjz/+uIYOHarmzZurSZMmWrRokb9DBwAAAHAG8XuxJEkjR47U7t27lZmZqX79+ikxMVFS+ZK8qkyaNElpaWnauXOnBgwYENBGDQAAAAAav4AUS5KUlJRU6/uOUlNTlZqaWk8RAQAAAEAFv9+zBAAAAADBgGIJAAAAADygWAIAAAAADyiWAAAAAMADiiUAAAAA8IBiCQAAAAA8oFgCAAAAAA8olgAAAADAA4olAAAAAPCAYgkAAAAAPKBYAgAAAAAPKJYAAAAAwIOwQAfgD8YYSZLD4QhwJJLT6VRBQYEcDofsdnugw0EQIXfgC/IGviBv4CtyB77wd964agJXjVCdM6JYys/PlyQlJycHOBIAAAAADUF+fr6aN29e7Tk2401JFeTKysr0zTffqFmzZrLZbAGNxeFwKDk5Wfv371dMTExAY0FwIXfgC/IGviBv4CtyB77wd94YY5Sfn682bdooJKT6u5LOiJmlkJAQtW3bNtBhVBITE8M/IvAJuQNfkDfwBXkDX5E78IU/86amGSUXGjwAAAAAgAcUSwAAAADgAcWSn0VEROjBBx9UREREoENBkCF34AvyBr4gb+Arcge+aMh5c0Y0eAAAAACA2mJmCQAAAAA8oFgCAAAAAA8olgAAAADAA4olAAAAAPCAYsmPsrOz1atXL8XFxWn69Omitwaq8p///EcdO3ZUWFiY+vTpo507d0oih+C9K664QosXL5ZE3sB7M2bM0PDhw61tcgfVefHFF9WuXTs1bdpUgwcP1t69eyWRN/Ds8OHDSklJsfJEqj5XGkoeUSz5SXFxsYYPH66ePXsqMzNTOTk51i8ywKm+/PJLjRs3TvPnz9fBgwfVvn17TZgwgRyC15YuXap33nlHEv/2wHvZ2dn629/+poULF0oid1C9L7/8Ug888ID+/e9/KycnR+3bt9ctt9xC3sCjQ4cO6eqrr65UKFWXKw0qjwz8Yvny5SYuLs4cP37cGGNMVlaWueSSSwIcFRqilStXmqefftraXrt2rQkPDyeH4JXDhw+bli1bmnPOOcc8//zz5A28UlZWZvr162dmz55t7SN3UJ1//etf5pe//KW1/cEHH5jWrVuTN/Do8ssvNwsXLjSSzJ49e4wx1f8b05DyiJklP9m+fbv69u2r6OhoSVK3bt2Uk5MT4KjQEF199dWaOHGitb1r1y6lpqaSQ/DKPffco1GjRqlv376S+LcH3nnmmWeUlZWllJQUvfnmm3I6neQOqtW1a1etXbtWn332mfLy8vTXv/5VQ4YMIW/gUUZGhu66665K+6rLlYaURxRLfuJwOJSSkmJt22w2hYaG6siRIwGMCg3diRMnlJ6erkmTJpFDqNG6dev0/vvv6w9/+IO1j7xBTY4dO6ZZs2apU6dOOnDggBYsWKD+/fuTO6hW165d9Ytf/EIXXnihYmNj9fHHHys9PZ28gUcdO3Z021ddrjSkPKJY8pOwsDBFRERU2hcZGamCgoIARYRgMGvWLDVt2lS33XYbOYRqFRUV6fbbb9fTTz+tmJgYaz95g5q88cYbOn78uNauXavZs2fr3Xff1dGjR/Xcc8+RO6jSli1btHLlSn388cfKz8/XmDFjNGzYMP7Ngdeqy5WGlEcUS34SHx+v3NzcSvvy8/MVHh4eoIjQ0K1Zs0Z///vf9fLLL8tut5NDqNbDDz+sXr166aqrrqq0n7xBTQ4cOKA+ffooPj5eUvkvMN26dVNRURG5gyr985//1OjRo9W7d281bdpUjzzyiL766iv+zYHXqsuVhpRHYX6/4hmqV69eevbZZ63tvXv3qri42Po/J+BUX331lX71q1/p6aefVteuXSWRQ6jeyy+/rNzcXMXGxkqSCgoK9Oqrr6pDhw5yOp3WeeQNfio5OVmFhYWV9u3bt0+PP/64/vznP1v7yB2cqqSkpNKSqPz8fB0/flxhYWHasmWLtZ+8QVWq+72mIf3Ow8ySn/Tv3195eXlasmSJJGn+/PkaPHiwQkNDAxwZGprCwkJdffXVGjlypK655hodO3ZMx44d06WXXkoOoUoffPCBsrOzlZWVpaysLI0YMUIPPfSQNm7cSN6gWldddZV27typv//97zpw4ICefPJJZWVlKS0tjdxBlS655BK98cYb+vOf/6yXX35ZI0eOVMuWLfXb3/6WvIFXqvvduEH93hyQHnxnqOXLl5uoqCjTokULc9ZZZ5ns7OxAh4QGaPny5UaS28+ePXvIIXjt5ptvNs8//7wxhn97ULPNmzebfv36maioKJOSkmKWL19ujCF3ULWysjIzd+5c065dO2O3202PHj1MZmamMYa8QdV0SutwY6rPlYaSRzZjeKyyPx08eFCZmZnq16+fEhMTAx0OghA5BF+QN/AVuQNfkDfwVnW50hDyiGIJAAAAADzgniUAAAAA8IBiCQAAAAA8oFgCAAAAAA8olgAAAADAA4olAAAAAPCAYgkA4Ffr169XbGxsoMOo1uLFi3XZZZcFOgwAQIBRLAEAGoQOHTpo/fr1fruezWbT3r17PR4bO3as3nzzTb/FAgBomMICHQAAAA1NeHi4wsPDAx0GACDAmFkCAATUFVdcIZvNpn379mngwIGy2WyaP3++dXz16tU6//zzFRsbqwkTJqi4uNg61qFDB7333nu6//771apVK23fvt069ve//13Jyclq1qyZRo4cqfz8fEnSz372M9lsNklSSkqKbDabXnnllUoxVbUM77XXXtM555yjhIQETZkyRUVFRZKkuXPn6pZbbtFDDz2k2NhYtW/fXh988IE1Lj09Xa1bt1ZMTIzGjBlT6T0AABouiiUAQEC9/vrrOnLkiJKTk7Vy5UodOXJEd999tyTpyy+/1DXXXKO7775bn376qT799FP96U9/qjR+9uzZ+uabb7Rs2TKdffbZkqQdO3ZoypQpev7557Vz50798MMP+tvf/iZJ2rp1q44cOSJJ2r59u44cOaLrrruuxjgzMzN188036w9/+IM2bdqkzMxMzZgxwzr+1ltv6X//+5+2bdumSy65RA888IAk6fPPP9eMGTP0z3/+U9u2bdP//vc/LV68+LQ/NwBA/WMZHgAgoJo0aSJJCgkJUdOmTSs1f1i2bJl69Oih3/zmN5KkiRMnatGiRZo1a5Z1TvPmzd2Kj06dOum7776T3W7XJ598ImOMvvjiC0lSs2bNrPNiYmK8bjbxzDPP6Fe/+pVGjhwpSVqwYIEGDx6sP//5z5Kk0NBQZWRkKDIyUrfccotuv/12SVJkZKQkqbi4WO3atdPHH3/s3QcDAAg4iiUAQIN18OBBbdu2zSpoSkpK1LRp00rn3HnnnW7jCgsLNWHCBG3YsEE9evRQWFiYSktLTyuW/fv3q3///tZ2x44dVVhYqEOHDkmSLr74YqswCg8PlzFGUvlSwWeffVYzZszQF198oSuuuEJ//etf1aJFi9OKBwBQ/1iGBwBoEEJCQqwCw6Vt27YaMWKEsrKylJWVpe3bt2vNmjWVznHNTJ3qiSeeUG5urr7//nutXbtWF198sds5NpvN7XrVadeunb766itr+8svv1R0dLQSEhIklc9SeXLgwAF169ZNn376qb7++msdOXJEDz/8sNfXBQAEDsUSAKBBSE1N1erVq/Xtt9/q/ffflySNGTNGH3zwgXbv3i2pvAgaN25cja917NgxGWN06NAhvfzyy3r66afdCqPU1FStWrVKBw8e1MaNG2t8zQkTJmjp0qX697//rV27dumee+7RbbfdZjWLqEpOTo6uvPJKffjhhzp+/LhsNpvKyspqvB4AIPAolgAADUJ6erpWr16tlJQUzZs3T1L5UrcXXnhB06ZN07nnnqvs7GwtW7asxte66667ZIxR586d9fzzz2v8+PHKysqqdM7f//53LVy4UKmpqfrHP/5R42tedNFFeuGFF/S73/1Ol1xyiXr27KnHHnusxnFpaWm6/fbb9ctf/lKdO3eWMcZq/gAAaNhspjZrEAAAAADgDMHMEgAAAAB4QLEEAAAAAB5QLAEAAACABxRLAAAAAOABxRIAAAAAeECxBAAAAAAeUCwBAAAAgAcUSwAAAADgAcUSAAAAAHhAsQQAAAAAHvw/c5kjcJ4RLJYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 生成模拟数据\n",
    "def generate_data(num_samples=100, noise_level=0.5):\n",
    "    \"\"\"\n",
    "    生成线性回归的模拟数据\n",
    "    y = 3x + 2 + 噪声\n",
    "    \"\"\"\n",
    "    np.random.seed(42)  # 设置随机种子以确保结果可重现\n",
    "    X = np.linspace(-5, 5, num_samples).reshape(-1, 1)\n",
    "    true_slope = 3\n",
    "    true_intercept = 2\n",
    "    y = true_slope * X + true_intercept + np.random.normal(0, noise_level, (num_samples, 1))\n",
    "    \n",
    "    return X, y, true_slope, true_intercept\n",
    "\n",
    "# 梯度下降算法实现线性回归\n",
    "def gradient_descent_linear_regression(X, y, learning_rate=0.01, num_iterations=1000):\n",
    "    \"\"\"\n",
    "    使用梯度下降法求解线性回归参数\n",
    "    \"\"\"\n",
    "    # 添加偏置项 (x0 = 1)\n",
    "    X_b = np.c_[np.ones((len(X), 1)), X]\n",
    "    \n",
    "    # 初始化参数\n",
    "    theta = np.random.randn(2, 1)\n",
    "    \n",
    "    # 存储每次迭代的损失值\n",
    "    losses = []\n",
    "    \n",
    "    # 梯度下降\n",
    "    for i in range(num_iterations):\n",
    "        # 计算预测值\n",
    "        y_pred = X_b.dot(theta)\n",
    "        \n",
    "        # 计算损失 (均方误差)\n",
    "        loss = (1/len(X)) * np.sum((y_pred - y)**2)\n",
    "        losses.append(loss)\n",
    "        \n",
    "        # 计算梯度\n",
    "        gradients = (2/len(X)) * X_b.T.dot(y_pred - y)\n",
    "        \n",
    "        # 更新参数\n",
    "        theta = theta - learning_rate * gradients\n",
    "        \n",
    "        # 每100次迭代打印一次损失\n",
    "        if i % 100 == 0:\n",
    "            print(f\"Iteration {i}: Loss = {loss:.4f}\")\n",
    "    \n",
    "    return theta, losses\n",
    "\n",
    "# 绘制结果\n",
    "def plot_results(X, y, theta, true_slope, true_intercept, losses):\n",
    "    \"\"\"\n",
    "    绘制数据和拟合结果\n",
    "    \"\"\"\n",
    "    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))\n",
    "    \n",
    "    # 绘制数据点和拟合线\n",
    "    ax1.scatter(X, y, alpha=0.7, label='Data points')\n",
    "    \n",
    "    # 绘制真实模型\n",
    "    x_range = np.linspace(min(X), max(X), 100)\n",
    "    y_true = true_slope * x_range + true_intercept\n",
    "    ax1.plot(x_range, y_true, 'r-', label='True model', linewidth=2)\n",
    "    \n",
    "    # 绘制拟合模型\n",
    "    y_pred = theta[1] * x_range + theta[0]\n",
    "    ax1.plot(x_range, y_pred, 'g--', label='Fitted model', linewidth=2)\n",
    "    \n",
    "    ax1.set_xlabel('X')\n",
    "    ax1.set_ylabel('y')\n",
    "    ax1.set_title('Linear Regression Fit')\n",
    "    ax1.legend()\n",
    "    ax1.grid(True)\n",
    "    \n",
    "    # 绘制损失曲线\n",
    "    ax2.plot(losses)\n",
    "    ax2.set_xlabel('Iterations')\n",
    "    ax2.set_ylabel('Loss')\n",
    "    ax2.set_title('Gradient Descent Convergence')\n",
    "    ax2.grid(True)\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "# 主函数\n",
    "if __name__ == \"__main__\":\n",
    "    # 生成数据\n",
    "    X, y, true_slope, true_intercept = generate_data(num_samples=100, noise_level=1.0)\n",
    "    \n",
    "    print(f\"True parameters: slope = {true_slope}, intercept = {true_intercept}\")\n",
    "    \n",
    "    # 使用梯度下降求解线性回归参数\n",
    "    theta, losses = gradient_descent_linear_regression(\n",
    "        X, y, learning_rate=0.01, num_iterations=1000\n",
    "    )\n",
    "    \n",
    "    print(f\"Estimated parameters: slope = {theta[1][0]:.4f}, intercept = {theta[0][0]:.4f}\")\n",
    "    \n",
    "    # 绘制结果\n",
    "    plot_results(X, y, theta, true_slope, true_intercept, losses)\n",
    "    \n",
    "    # 研究不同学习率对收敛的影响\n",
    "    learning_rates = [0.001, 0.01, 0.1, 0.5]\n",
    "    plt.figure(figsize=(10, 6))\n",
    "    \n",
    "    for lr in learning_rates:\n",
    "        _, losses = gradient_descent_linear_regression(\n",
    "            X, y, learning_rate=lr, num_iterations=100\n",
    "        )\n",
    "        plt.plot(losses[:100], label=f\"LR = {lr}\")\n",
    "    \n",
    "    plt.xlabel('Iterations')\n",
    "    plt.ylabel('Loss')\n",
    "    plt.title('Effect of Learning Rate on Convergence')\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9656bb7b-125f-4cc0-8bd4-923afd493a55",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:base] *",
   "language": "python",
   "name": "conda-base-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
